Hi, Jonathon,
The other guys have given great info on your question - I have only 2 points to add.
But first: Get Rick's book, "Catamaran Racing: for the Nineties" Rick covers all this lucidly, with supporting detail, historical research, equal time to opposing points of view, etc.
Okay, "Running down" you can get to any point directly downwind of you faster by sailing aproximately 45 deg. above straight downwind - but the apparant wind will be a beam reach! You'll equal or exceed the wind speed on this heading, so if you suddenly turn downwind, you'll experience virtual calm, while speeding along. There's a sudden drop off, about when the apparant wind crosses forward of the beam, and turning down, "driving off" etc is how you get there - and it's a great escape from a big puff.
So to run downwind reeeeeal fast: Sail about 45 deg above straight-downwind. Set your traveler at either the leeward footstrap, or the inboard side of the leeward hull, I've heard both schools of thought Use leach tells low and high to set your main's twist. The main will need more twist offwind than upwind, as the small difference between windspeed aloft and near the surface produces a large change in apparant wind between the top of the sail and he bottom. Sail a course around 45 deg above straight-downwind, and hunt with your helm until you find the "turbo" spot. Now sail that line and look at your tells and tweak the sheets until they all break and flow simultaneously.
Like the man said, practice using that dropoff to escape from puffs- your upwind reflex to head up in times of trouble can surprise you with wet results.